Question

A small spherical ball of radius 0.1 mm and density 10⁴ kg m^-3 falls freely under gravity through a distance of h before entering a tank of water. If, after entering the water the velocity of the ball does not change and it continues to fall with the same constant velocity inside the water, then the value of h will be ______ m.

(Given g = 10 ms^-2, the viscosity of water = 1.0 × 10^-5 N-sm^-2).

Options

• 19

• 21

• 20

• 22

Answer 1

A small spherical ball of radius 0.1 mm and density 10⁴ kg m^-3 falls freely under gravity through a distance of h before entering a tank of water. If, after entering the water the velocity of the ball does not change and it continues to fall with the same constant velocity inside the water, then the value of h will be 20 m.

Explanation:

As the terminal speed,

`v = sqrt(2gh) = 2/9 (r^2g(ρ - ρ^'))/η`

= `2/9 xx (10^-8 xx 10 xx 9000)/(10^-5)`

= `2/9 xx 9 xx 10`

`sqrt(2gh)` = 20

⇒ `h = 400/(2g)`

h = 20 m